ODE
\[ x^4 y''''(x)+6 x^3 y'''(x)+4 x^2 y''(x)-2 x y'(x)-4 y(x)=0 \] ODE Classification
[[_high_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.167839 (sec), leaf count = 30
\[\left \{\left \{y(x)\to c_4 x^2+\frac {c_3}{x^2}+c_1 \cos (\log (x))+c_2 \sin (\log (x))\right \}\right \}\]
Maple ✓
cpu = 0.016 (sec), leaf count = 25
\[\left [y \left (x \right ) = \frac {\textit {\_C1}}{x^{2}}+x^{2} \textit {\_C2} +\textit {\_C3} \sin \left (\ln \left (x \right )\right )+\textit {\_C4} \cos \left (\ln \left (x \right )\right )\right ]\] Mathematica raw input
DSolve[-4*y[x] - 2*x*y'[x] + 4*x^2*y''[x] + 6*x^3*y'''[x] + x^4*y''''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[3]/x^2 + x^2*C[4] + C[1]*Cos[Log[x]] + C[2]*Sin[Log[x]]}}
Maple raw input
dsolve(x^4*diff(diff(diff(diff(y(x),x),x),x),x)+6*x^3*diff(diff(diff(y(x),x),x),x)+4*x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)-4*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1/x^2+x^2*_C2+_C3*sin(ln(x))+_C4*cos(ln(x))]